Characterisation of main classes of fuzzy relations using fuzzy modal operators

Fuzzy modal operators express interactions between binary fuzzy relations and fuzzy sets. Each of these operators is determined by a binary fuzzy relation (on a given universe) and transforms one fuzzy set (in this universe) to another one. In this paper, we define several fuzzy modal operators and provide characterisations of main classes of binary fuzzy relations by means of these operators. Interpretation of these characterisations is presented in the context of fuzzy modal logics. We show that these characterisations constitute the basis for determining characteristic axioms of particular classes of fuzzy modal logics.